On a nonlinear generalized max-type difference equation

The boundedness character of positive solutions of the following max-type difference equation x n = max { A , x n − 1 p x n − k r } , n ∈ N 0 , where k ∈ N ∖ { 1 } , the parameters A and r are positive and p is a nonnegative real number is studied in this paper. Our main results considerably improve results appearing in the literature.